Turnstile (symbol)

In mathematical logic and computer science the symbol has taken the name turnstile because of its resemblance to a typical turnstile if viewed from above. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails". The symbol was first used by Gottlob Frege in his 1879 book on logic, Begriffsschrift.

Martin-Löf analyzes the symbol thus: "...[T]he combination of Frege's Urteilsstrich, judgement stroke [ | ], and Inhaltsstrich, content stroke [—], came to be called the assertion sign." Frege's notation for a judgement of some content

can be then be read

In the same vein, a conditional assertion

can be read as:

In TeX, the turnstile symbol is obtained from the command \vdash. In Unicode, the turnstile symbol (⊢) is called right tack and is at code point U+22A2. On a typewriter, a turnstile can be composed from a vertical bar (|) and a dash (–). In LaTeX there is a turnstile package which issues this sign in many ways, and is capable of putting labels below or above it, in the correct places.

Right Tack

Right Tack (1966–1985) was an Irish-bred, British-trained Thoroughbred racehorse and sire. In a career that lasted from June 1968 to October 1969 he ran twelve times, winning eight races and finishing second three times. As a two-year-old he won his last five races included the Middle Park Stakes and was rated the second-best British colt of his generation. In the following year he became the first horse to win both the 2000 Guineas at Newmarket and the Irish 2000 Guineas at the Curragh. After being retired from racing he stood as a breeding stallion in Ireland and Australia.

Background

Right Tack was a bay horse bred in County Meath, Ireland by Paul Larkin. As a weanling he was sent to the Dublin November sales where he was bought for 700 guineas by Philip O'Dwyer. A year later O'Dwyer was able to make a profit on the deal when he sold Right Tack for 3,200 guineas at the Doncaster yearling sale. The colt was bought by bloodstock agents acting on behalf of Jim Brown, a Dublin-based Englishman who sent him to be trained at Epsom by John Sutcliffe.